Earnest Money and Option Fee are similar
TREC rules covering this section of the act state: "Unless a different time to deposit money is expressly agreed upon in writing by the principals to the transaction, 'reasonable time' as used in this section means by the close of business of the second working day after execution of the contract by the principals." (Section 535.159(i))
The promulgated contract form in paragraph 5 covering Earnest Money has no wording about time of delivery (unlike paragraph 23 for the Option Fee). However, "reasonable time" as quoted for Earnest Money has been long established as 2nd business day after execution.
Option Fee delivery, while similar in nature (it is a contract to grant exclusive right to buy to the buyer for a period of time - and needs to be paid for), does state exactly that the fee must be delivered within 2 days. It doesn't say "business" days, just days. While it can be delivered to the agent for the seller or the seller, it should not be delivered to a title company or escrow agent.
This confuses some people, because they think they have 2 business days for the Option Fee delivery. Who can say how litigation will turn out? An attorney is your best bet, if you're confused.
deliver Earnest Money to escrow agent by close of business the 2nd business day after Execution
deliver Option Fee to seller's agent with the contract but not later than 2nd calendar day after Execution
If Buyer is remote and cannot deliver funds, you should consider these possibilities:
have Buyer send cashier's check by overnight or wire transfer
in special provisions document the delivery method for the option fee
have Buyer's agent pick up and deliver check from local bank